Annotation of gforth/float.fs, revision 1.51

1.1       anton       1: \ High level floating point                            14jan94py
                      2: 
1.50      anton       3: \ Copyright (C) 1995,1997,2003,2004,2005,2006 Free Software Foundation, Inc.
1.18      anton       4: 
                      5: \ This file is part of Gforth.
                      6: 
                      7: \ Gforth is free software; you can redistribute it and/or
                      8: \ modify it under the terms of the GNU General Public License
                      9: \ as published by the Free Software Foundation; either version 2
                     10: \ of the License, or (at your option) any later version.
                     11: 
                     12: \ This program is distributed in the hope that it will be useful,
                     13: \ but WITHOUT ANY WARRANTY; without even the implied warranty of
                     14: \ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
                     15: \ GNU General Public License for more details.
                     16: 
                     17: \ You should have received a copy of the GNU General Public License
                     18: \ along with this program; if not, write to the Free Software
1.34      anton      19: \ Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111, USA.
1.18      anton      20: 
1.17      anton      21: \ 1 cells 4 = [IF]
                     22: \ ' cells   Alias sfloats
                     23: \ ' cell+   Alias sfloat+
                     24: \ ' align   Alias sfalign
                     25: \ ' aligned Alias sfaligned
                     26: \ [ELSE]
                     27: \ : sfloats  2* 2* ;
                     28: \ : sfloat+  4 + ;
                     29: \ : sfaligned ( addr -- addr' )  3 + -4 and ;
                     30: \ : sfalign ( -- )  here dup sfaligned swap ?DO  bl c,  LOOP ;
                     31: \ [THEN]
1.6       pazsan     32: 
1.17      anton      33: \ 1 floats 8 = [IF]
                     34: \ ' floats   Alias dfloats
                     35: \ ' float+   Alias dfloat+
                     36: \ ' falign   Alias dfalign
                     37: \ ' faligned Alias dfaligned
                     38: \ [ELSE]
                     39: \ : dfloats  2* 2* 2* ;
                     40: \ : dfloat+  8 + ;
                     41: \ : dfaligned ( addr -- addr' )  7 + -8 and ;
                     42: \ : dfalign ( -- )  here dup dfaligned swap ?DO  bl c,  LOOP ;
                     43: \ [THEN]
                     44: 
                     45: : sfalign ( -- ) \ float-ext s-f-align
1.26      crook      46:     \G If the data-space pointer is not single-float-aligned, reserve
                     47:     \G enough space to align it.
1.17      anton      48:     here dup sfaligned swap ?DO  bl c,  LOOP ;
                     49: : dfalign ( -- ) \ float-ext d-f-align
1.26      crook      50:     \G If the data-space pointer is not double-float-aligned, reserve
                     51:     \G enough space to align it.
1.17      anton      52:     here dup dfaligned swap ?DO  bl c,  LOOP ;
                     53: 
1.51    ! anton      54: (Field) sfloat+ ( sf-addr1 -- sf-addr2 ) \ float-ext s-float-plus
1.31      anton      55: \G @code{1 sfloats +}.
1.51    ! anton      56:     1 sfloats ,
1.17      anton      57: 
1.51    ! anton      58: (Field) dfloat+ ( df-addr1 -- df-addr2 ) \ float-ext d-float-plus
1.31      anton      59: \G @code{1 dfloats +}.
1.51    ! anton      60:     1 dfloats ,
        !            61:     
1.26      crook      62: : f, ( f -- ) \ gforth
                     63:     \G Reserve data space for one floating-point number and store
                     64:     \G @i{f} in the space.
                     65:     here 1 floats allot f! ;
1.1       anton      66: 
1.29      crook      67: : fconstant  ( r "name" -- ) \ float f-constant
1.13      anton      68:     Create f,
1.16      anton      69: DOES> ( -- r )
                     70:     f@ ;
1.1       anton      71: 
1.29      crook      72: : fdepth ( -- +n ) \ float f-depth
1.28      crook      73:     \G @i{+n} is the current number of (floating-point) values on the
1.24      crook      74:     \G floating-point stack.
                     75:     fp0 @ fp@ - [ 1 floats ] Literal / ;
1.1       anton      76: 
1.29      crook      77: : FLiteral ( compilation r -- ; run-time -- r ) \ float f-literal
1.28      crook      78:     \G Compile appropriate code such that, at run-time, @i{r} is placed
1.24      crook      79:     \G on the (floating-point) stack. Interpretation semantics are undefined.
1.39      anton      80:     BEGIN  here cell+ cell+ dup faligned <>  WHILE  postpone noop  REPEAT
                     81:     postpone ahead here >r f, postpone then
                     82:     r> postpone literal postpone f@ ;  immediate
1.24      crook      83: 
1.29      crook      84: &15 Value precision ( -- u ) \ float-ext
1.28      crook      85: \G @i{u} is the number of significant digits currently used by
1.24      crook      86: \G @code{F.} @code{FE.} and @code{FS.} 
1.29      crook      87: : set-precision ( u -- ) \ float-ext
1.24      crook      88:     \G Set the number of significant digits currently used by
1.28      crook      89:     \G @code{F.} @code{FE.} and @code{FS.} to @i{u}.
1.24      crook      90:     to precision ;
1.1       anton      91: 
                     92: : scratch ( r -- addr len )
                     93:   pad precision - precision ;
                     94: 
                     95: : zeros ( n -- )   0 max 0 ?DO  '0 emit  LOOP ;
                     96: 
                     97: : -zeros ( addr u -- addr' u' )
                     98:   BEGIN  dup  WHILE  1- 2dup + c@ '0 <>  UNTIL  1+  THEN ;
                     99: 
1.4       pazsan    100: : f$ ( f -- n )  scratch represent 0=
                    101:   IF  2drop  scratch 3 min type  rdrop  EXIT  THEN
                    102:   IF  '- emit  THEN ;
                    103: 
1.29      crook     104: : f.  ( r -- ) \ float-ext f-dot
1.32      anton     105: \G Display (the floating-point number) @i{r} without exponent,
1.24      crook     106: \G followed by a space.
1.35      anton     107:   f$ dup >r 0<=
1.4       pazsan    108:   IF    '0 emit
1.1       anton     109:   ELSE  scratch r@ min type  r@ precision - zeros  THEN
                    110:   '. emit r@ negate zeros
                    111:   scratch r> 0 max /string 0 max -zeros type space ;
1.3       benschop  112: \ I'm afraid this does not really implement ansi semantics wrt precision.
                    113: \ Shouldn't precision indicate the number of places shown after the point?
1.1       anton     114: 
1.33      anton     115: \ Why do you think so? ANS Forth appears ambiguous on this point. -anton.
                    116: 
1.29      crook     117: : fe. ( r -- ) \ float-ext f-e-dot
1.32      anton     118: \G Display @i{r} using engineering notation (with exponent dividable
                    119: \G by 3), followed by a space.
1.24      crook     120:   f$ 1- s>d 3 fm/mod 3 * >r 1+ >r
1.33      anton     121:   scratch r@ tuck min tuck - >r type r> zeros
                    122:   '. emit scratch r> /string type
1.1       anton     123:   'E emit r> . ;
                    124: 
1.29      crook     125: : fs. ( r -- ) \ float-ext f-s-dot
1.32      anton     126: \G Display @i{r} using scientific notation (with exponent), followed
                    127: \G by a space.
1.24      crook     128:   f$ 1-
1.4       pazsan    129:   scratch over c@ emit '. emit 1 /string type
                    130:   'E emit . ;
                    131: 
1.19      anton     132: : sfnumber ( c-addr u -- r true | false )
                    133:     2dup [CHAR] e scan ( c-addr u c-addr2 u2 )
1.16      anton     134:     dup 0=
                    135:     IF
1.19      anton     136:        2drop 2dup [CHAR] E scan ( c-addr u c-addr3 u3 )
1.16      anton     137:     THEN
                    138:     nip
1.7       anton     139:     IF
1.19      anton     140:        >float
                    141:     ELSE
                    142:        2drop false
                    143:     THEN ;
                    144: 
1.47      anton     145: [ifundef] compiler-notfound1
                    146: defer compiler-notfound1
                    147: ' no.extensions IS compiler-notfound1
                    148: 
                    149: :noname compiler-notfound1 execute ; is compiler-notfound
                    150: 
                    151: defer interpreter-notfound1
                    152: ' no.extensions IS interpreter-notfound1
                    153: 
                    154: :noname interpreter-notfound1 execute ; is interpreter-notfound
                    155: [then]
                    156: 
                    157: :noname ( c-addr u -- ... xt )
1.19      anton     158:     2dup sfnumber
                    159:     IF
1.47      anton     160:        2drop [comp'] FLiteral
1.19      anton     161:     ELSE
1.47      anton     162:        defers compiler-notfound1
1.19      anton     163:     ENDIF ;
1.47      anton     164: IS compiler-notfound1
1.1       anton     165: 
1.47      anton     166: :noname ( c-addr u -- ... xt )
1.19      anton     167:     2dup sfnumber
                    168:     IF
1.47      anton     169:        2drop ['] noop
1.19      anton     170:     ELSE
1.47      anton     171:        defers interpreter-notfound1
1.19      anton     172:     ENDIF ;
1.47      anton     173: IS interpreter-notfound1
1.13      anton     174: 
1.29      crook     175: : fvariable ( "name" -- ) \ float f-variable
1.15      pazsan    176:     Create 0.0E0 f, ;
1.13      anton     177:     \ does> ( -- f-addr )
1.1       anton     178: 
1.24      crook     179: 1.0e0 fasin 2.0e0 f* fconstant pi ( -- r ) \ gforth
1.28      crook     180: \G @code{Fconstant} -- @i{r} is the value pi; the ratio of a circle's area
1.24      crook     181: \G to its diameter.
                    182: 
                    183: : f2* ( r1 -- r2 ) \ gforth
1.28      crook     184:     \G Multiply @i{r1} by 2.0e0
1.24      crook     185:     2.0e0 f* ;
                    186: 
                    187: : f2/ ( r1 -- r2 ) \ gforth
1.28      crook     188:     \G Multiply @i{r1} by 0.5e0
1.24      crook     189:     0.5e0 f* ;
                    190: 
                    191: : 1/f ( r1 -- r2 ) \ gforth
1.28      crook     192:     \G Divide 1.0e0 by @i{r1}.
1.24      crook     193:     1.0e0 fswap f/ ;
1.6       pazsan    194: 
1.36      pazsan    195: get-current environment-wordlist set-current
                    196: 1.7976931348623157e308 FConstant max-float
                    197: set-current
1.6       pazsan    198: 
1.10      anton     199: \ We now have primitives for these, so we need not define them
1.6       pazsan    200: 
1.15      pazsan    201: \ : falog ( f -- 10^f )  [ 10.0e0 fln ] FLiteral f* fexp ;
1.10      anton     202: 
1.15      pazsan    203: \ : fsinh    fexpm1 fdup fdup 1.0e0 f+ f/ f+ f2/ ;
1.10      anton     204: \ : fcosh    fexp fdup 1/f f+ f2/ ;
1.15      pazsan    205: \ : ftanh    f2* fexpm1 fdup 2.0e0 f+ f/ ;
1.10      anton     206: 
1.15      pazsan    207: \ : fatanh   fdup f0< >r fabs 1.0e0 fover f- f/  f2* flnp1 f2/
1.10      anton     208: \            r> IF  fnegate  THEN ;
1.15      pazsan    209: \ : facosh   fdup fdup f* 1.0e0 f- fsqrt f+ fln ;
                    210: \ : fasinh   fdup fdup f* 1.0e0 f+ fsqrt f/ fatanh ;
1.9       pazsan    211: 
1.27      anton     212: : f~abs ( r1 r2 r3 -- flag ) \ gforth
                    213:     \G Approximate equality with absolute error: |r1-r2|<r3.
                    214:     frot frot f- fabs fswap f< ;
                    215: 
                    216: : f~rel ( r1 r2 r3 -- flag ) \ gforth
                    217:     \G Approximate equality with relative error: |r1-r2|<r3*|r1+r2|.
                    218:        frot frot fover fabs fover fabs f+ frot frot
                    219:        f- fabs frot frot f* f< ;
                    220: 
1.29      crook     221: : f~ ( r1 r2 r3 -- flag ) \ float-ext f-proximate
1.31      anton     222:     \G ANS Forth medley for comparing r1 and r2 for equality: r3>0:
                    223:     \G @code{f~abs}; r3=0: bitwise comparison; r3<0: @code{fnegate f~rel}.
1.16      anton     224:     fdup f0=
1.31      anton     225:     IF \ bitwise comparison
1.41      anton     226:        fp@ float+ 1 floats over float+ over str=
1.31      anton     227:        fdrop fdrop fdrop
1.27      anton     228:        EXIT
1.16      anton     229:     THEN
                    230:     fdup f0>
                    231:     IF
1.27      anton     232:        f~abs
1.16      anton     233:     ELSE
1.27      anton     234:        fnegate f~rel
                    235:     THEN ;
1.44      anton     236: 
                    237: \ proposals from Krishna Myeni in <cjsp2d$47l$1@ngspool-d02.news.aol.com>
                    238: \ not sure if they are a good idea
                    239: 
                    240: : FTRUNC ( r1 -- r2 )
                    241:     \ round towards 0
                    242:     \ !! should be implemented properly
                    243:     F>D D>F ;
                    244: 
                    245: : FMOD ( r1 r2 -- r )
                    246:     \ remainder of r1/r2
                    247:     FOVER FOVER F/ ftrunc F* F- ;

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